Least Common Multiple (LCM) of 61 and 100
The least common multiple (LCM) of 61 and 100 is 6100.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 61 and 100?
First, calculate the GCD of 61 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 100 = 0 remainder 61 |
| 2 | 100 ÷ 61 = 1 remainder 39 |
| 3 | 61 ÷ 39 = 1 remainder 22 |
| 4 | 39 ÷ 22 = 1 remainder 17 |
| 5 | 22 ÷ 17 = 1 remainder 5 |
| 6 | 17 ÷ 5 = 3 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 57 | 9975 |
| 134 and 130 | 8710 |
| 99 and 101 | 9999 |
| 56 and 161 | 1288 |
| 114 and 135 | 5130 |